Distributed Discovery of Large Near-Cliques

Given an undirected graph and 0 ≤ ≤ 1, a set of nodes is called -near clique if all but an fraction of the pairs of nodes in the set have a link between them. In this paper we present a fast synchronous network algorithm that uses small messages and finds a near-clique. Specifically, we present a constant-time algorithm that finds, with constant probability of success, a linear size -near clique if there exists an 3 -near clique clique of linear size in the graph. The algorithm uses messages of O(log n) bits. The failure probability can be reduced to n−Ω(1) in O(log n) time, and the algorithm also works if the graph contains a clique of size Ω(n/ log log n). Our approach is based on a new idea of adapting property testing algorithms to the distributed setting. ∗ Supported in part by the Israel Science Foundation, grant 664/05. 

• Type: Conference
• Year: 2009
• Where: WDAG
• Authors: Zvika Brakerski, Boaz Patt-Shamir
• Keywords: -near Clique, Algorithms, Size -near Clique, WDAG 2009